Höllig, KlausOverview
Publication Timeline
Most widely held works by
Klaus Höllig
Finite element methods with Bsplines
by Klaus Höllig
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11 editions published between 2003 and 2010 in English and held by 452 WorldCat member libraries worldwide Finite Element Methods with BSplines describes new weighted approximation techniques, combining the computational advantages of Bsplines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for Bsplines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples
Box splines
by Carl De Boor
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Book
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11 editions published between 1993 and 2010 in English and Undetermined and held by 394 WorldCat member libraries worldwide This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an uptodate bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasiinterpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms
Grundlagen der Numerik
by Klaus Höllig
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Book
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1 edition published in 1998 in German and held by 29 WorldCat member libraries worldwide
Approximation and modeling with Bsplines
by Klaus Höllig
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Book
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2 editions published in 2013 in English and held by 24 WorldCat member libraries worldwide
Nonuniform WEBSplines
by Klaus Höllig
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3 editions published in 2002 in English and held by 15 WorldCat member libraries worldwide
Error estimates for the webmethod
by Klaus Höllig
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Book
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3 editions published in 2000 in English and held by 8 WorldCat member libraries worldwide
Multivariate splines
by Klaus Höllig
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Book
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5 editions published between 1981 and 1987 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Bsplines without divided differences
by Mathematics Research Center (United States. Army)
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Book
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6 editions published in 1985 in English and Undetermined and held by 5 WorldCat member libraries worldwide This note develops the basic Bspline theory without using divided differences. Instead, the starting point is the definition of Bsplines via recurrence relations. This approach yields very simple derivations of basic properties of spline functions and algorithms
Convergence of cardinal series
by Carl De Boor
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Book
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3 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
Boxspline tilings
by Carl De Boor
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Book
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2 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide
Geometric hermite interpolation with maximal order and smoothness
by Klaus Höllig
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Book
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2 editions published between 1995 and 1996 in English and held by 4 WorldCat member libraries worldwide
Box splines
by Klaus Höllig
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Book
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2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Approximationszahlen von SobolevEinbettungen
by Klaus Höllig
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Book
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2 editions published in 1979 in German and held by 3 WorldCat member libraries worldwide
Divided differences, hyperbolic equations, and lifting distributions
by Klaus Höllig
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Book
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2 editions published in 1985 in English and held by 3 WorldCat member libraries worldwide
Geometric continuity of spline curves and surfaces
by Klaus Höllig
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Book
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2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
L∞boundedness of L2projections on splines for a geometric mesh
by Klaus Höllig
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Book
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2 editions published in 1980 in English and held by 3 WorldCat member libraries worldwide
A generalization of Jackson's inequality
by Klaus Höllig
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Book
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2 editions published in 1980 in German and English and held by 2 WorldCat member libraries worldwide
A Diffusion Equation with a Nonmonotone Constitutive Function
by Mathematics Research Center (United States. Army)
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Book
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2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide In this report we first review known (previously unpublished) a priori estimates for (P), and we then give a simpler construction for the existence of infinitely many solution of (P) for a piecewise linear phi as suggested by G. Strang. we then investigate further the qualitative behavior of solutions of (P). Motivated by known results in one space dimension for the steady state, nonelliptic problem, we study the analogous convexified problem associated with (P). Analytical and numerical considerations suggest that the unique solution of the convexified problem (which has a monotone, nondecreasing constitutive function) can be interpreted as an average of solutions of (P), whenever the data f'(.) reach the critical range
Minimal support for bivariate splines
by Mathematics Research Center (United States. Army)
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Book
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3 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide In earlier works the authors applied their results on boxsplines to analyze the approximation properties of bivariate smooth piecewise polynomials on the three direction mesh. In this report they obtain similar results for the other natural triangulation of R sub 2 which is generated by four directions. In particular they extend their results of minimality of support which are useful for constructing bases with good computational properties. Keywords: Numerical analysis
A Singular Free Boundary Problem
by Mathematics Research Center (United States. Army)
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Book
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2 editions published in 1983 in Undetermined and English and held by 2 WorldCat member libraries worldwide The Cauchy problem is similar to the wellknown one phase Stefan problem (inone space dimension). In the latter one would assume g(x) = 1 for x <0, as well as g(x)> 0 for x> 0, so that g would have a jump discontinuity at x = 0. Our assumptions on the initial data g yield a different behavior of the solution v and of the resulting free boundary. Indeed, the free boundary is not (infinitely) differentiable at t = 0, contrary to the situation for the classical Stefan problem. This problem also serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi. That analysis shows the existence of infinitely many solutions v of the nonmonotone problem each having v bounded, but oscillating more and more rapidly as t infinity 0(+). Thus each solution v exhibits phase changes. Numerical experiments further suggest the conjecture that the physically correct solution of the nonmonotone problem is the one which for t> 0 sufficiently large approaches the unique solution of the appropriately related convexified monotone problem. This paper is another step towards the understanding of this intriguing phenomenon more
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Algorithms Approximation theory Computer scienceMathematics Differential equations, Hyperbolic EngineeringMathematical models Finite element method Fourier series Global analysis (Mathematics) Interpolation Mathematical models Mathematics Multivariate analysis Numerical analysis Splines Spline theory Structural analysis (Engineering) Surfaces Tiling (Mathematics)

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Höllig K.
Höllig, K. (Klaus)
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